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A researcher wants to investigate the effects of environmental factors on IQ scores. For an...

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A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 52.5% of them have an IQ score over 100. It is known that 50% of the general population has an IQ score exceeding 100.Answer the following. (If necessary, consult a list of formulas.)(a) Find the mean of p, where is the proportion of people with IQ scores over 100 in a random sample of 400 people.(b) Find the standard deviation of p.(c) Compute an approximation for P(?0.525), which is the probability that there will be 52.5% or more individuals with IQ scores over 100 in a random sample of 400. Round your answer to four decimal places.

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